Problem: Simplify the following expression and state the condition under which the simplification is valid. $n = \dfrac{y^2 - 49}{y + 7}$
Explanation: First factor the polynomial in the numerator. The numerator is in the form ${a^2} - {b^2}$ , which is a difference of two squares so we can factor it as $({a} + {b})({a} - {b})$ $ a = y$ $ b = \sqrt{49} = 7$ So we can rewrite the expression as: $n = \dfrac{({y} + {7})({y} {-7})} {y + 7} $ We can divide the numerator and denominator by $(y + 7)$ on condition that $y \neq -7$ Therefore $n = y - 7; y \neq -7$